The Commutant Lifting Theorem
Ciprian Foiaş, Arthur E. Frazho · Birkhäuser Basel eBooks · 1990
In this chapter we will introduce the main theorem of this monograph, namely, the Commutant Lifting Theorem and we will give several different proofs for it. Each proof illuminates different features of this theorem. We also use the second proof to discuss the uniqueness question in the commutant lifting theorem. The third proof establishes the connection to Ando’s dilation theorem for two commuting contractions, while the fourth proof is based on Arocena’s coupling of contractions. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.